Method of forming a cylindrical dielectric lens



CROSS REFERENCE EXAMtNER R. L. HORST June 14, 1966 METHOD OF FORMING ACYLINDRIGAL DIELECTRIC LENS Original Filed July 11, 1962 Hopper withPctystyrene Beads pp wHh polysyrene Beads Variable Contour Plus Aiurn.Slivers A 2 m F Vacuum Exhaust FIG 2C.

To Stabilization Room INVENTOR Robert L. Horst Qafij ATTORNEYS UnitedStates Patent 11 Claims. (Cl. 26445) This application is a division ofmy prior copending application Serial No. 209,075, filed July 11, 1962for Three-Dimensional Dielectric Lens and Method of Forming the Same,now abandoned.

The present invention relates to the fabrication of an improveddielectric lens, e.g., a Luneberg lens, a Maxwell lens, a Kelleher lens,or the like, characterized by a dielectric constant and hence arefractive index which varies substantially continuously as a functionof the lens radial coordinate. In this respect, the lens of the presentinvention distinguishes from so-called step-function lenses which havebeen produced heretofore in that, through a continuous grading ofdielectric constant, the novel monolithic lens of the present inventionis adapted to effect a performance more nearly approaching theoreticalperformances than has been possible heretofore.

During the last decade, there have been numerous attempts at thefabrication of high quality dielectric lenses for use at high radiofrequency, and particularly at frequencies in the microwave portion ofthe spectrum. One such dielectric lens suggested heretofore is theso-called Luneberg lens, a lens which may take the form of either acylindrical two-dimensional lens or a spherical threedimensional device,depending upon the focus desired and the configuration of the feed hornor antenna. In such a lens, for example of the cylindrical type,Luneberg has shown that, in theory, if electromagnetic energy in theform of a plane wave impinges upon the device, said electromagneticenergy will be refracted and concentrated as a line focus along a linegenerally parallel to the axis of the lens and located at the surface ofthe lens. In order for the lens to operate in this manner, Luneberg hasfurther shown that the refractive index (n) of the lens must vary as afunction of the radial coordinate (r) of the lens according to anequation which reduces to:

where R is the lens radius. Based upon the results of Lunebergs work,subsequent workers in the field have shown that by appropriatemodification of the dielectric gradation, the actual position of thefocus at the lens (Luneberg has shown that a second focus would alsoexist, in theory, at infinity) may be shifted to other positions eitherinterior of the lens or spaced externally of the lens surface.

As will be appreciated from the formula given above, the dielectricconstant or refractive index of the lens should vary continuously as afunction of the lens radial coordinate if operation according to thetheoretical is to be achieved. To the present time, however, nopractical techniques have been suggested for fabricating a dielectriclens having such a continuously varying dielectric constant.Accordingly, it is the practice at the present time to fabricate suchlenses by assembling various lens subcomponents (e.g., blocks ofmaterial, concentric cylinders, or shells, etc.) to effect a step-wiseapproximation of the theoretical refractive index gradation.

These step construction techniques, prevalent at the present time, areaccompanied by a number of distinct disadvantages. For example, the veryfact that the lenses are assembled from a plurality of subcomponents orconstructional modules having different dielectric constants necessarilyresults in dielectric discontinuities at the abutting junctions of thesubcomponents, with attendant reflections and losses at thesediscontinuities; and these losses and reflections are aggravated bypossible physical discontinuities (air gaps, cement joints, etc.) atsaid subcomponent junctions produced during assembly of the overalllens. Refinement of such a lens necessitates reduction of the dielectricstep size, thereby requiring constructional modules of smallerdimensions. The consequent increase in the number of modules employedobviously serves to further complicate the interface problem, in that amultiplicity of junctions exists, each of which represents a dielectricdiscontinuity and as such is a reflecting plane. The fractionalreflected power for wave (normal) incidence at such dielectric interfaceis described by the well-known relationship where R is the reflectioncoeflicient and n 11 are the refractive indices of the two mediums.Similar expressions describe reflection for arbitrary angles ofincidence and are presented in many texts on electromagnetic fieldtheory, e.g., Electromagnetic Fields and Waves- R. V. Langmuir. Theundesired reflections always accompany the desired wave refraction, andare by no means insignificant as can be seen by evaluation of theequations noted.

A further disadvantage is that a step constructed lens of typessuggested heretofore, must be assembled; and such assembly steps areextremely time-consuming and costly procedures if extraneous physicaldiscontinuities are to be minimized. Moreover, the assembly techniquesemployed heretofore necessarily require that lens testing procedures bedeferred until after the lens has been completely assembled; and thereis no way to evaluate the final lens structure, as a lens, without firstexpending time and money in assembly.

Finally, notwithstanding all of these difliculties, the resultingstep-function lens, even if carefully made, necessarily does not conformto theoretical operation since, by the very nature of the lens, itcomprises a stepped dielectric gradation rather than a continuouslyvarying gradation.

The present invention obviates the various problems mentioned, andproduces a novel lens structure wherein the lens dielectric constantvaries continuously as a function of the lens radial coordinate inaccordance with any particular formula which may be selected for aparticular lens. A novel lens is thus provided which receives andtransmits electromagnetic radiation in a pattern more closelyapproximating that calculated by theory than has been possibleheretofore. Moreover, the present invention achieves this result by anovel fabrication technique which directly produces a lens having thedesired continuous variation without requiring assembly steps. The lensof the present invention may therefore be evaluated as a lensimmediately after completion of its fabrication, without the necessityof expending the considerable time and costs attendant lens assemblyprocedures normally employed heretofore.

It is accordingly an object of the present invention to provide a methodof fabricating an improved mass of dielectric material, particularly adielectric lens, having a dielectric constant which exhibits a smoothlyvarying gradation in accordance with any desired formula characteristic,for example, of a particular lens to be produced. In the specificexample to be described hereinafter, the fabrication of a Luneberg lenswill be described, and more particularly, a Luneberg lens of thecylindrical type; but as will be apparent, the techniques here involvedmay be utilized in the fabrication of masses having other physical andmathematical (or optical) configurations.

Another object of the present invention resides in the provision of amethod of fabricating an improved dielectric lens eliminating dielectricdiscontinuities, wave reflections, and energy losses which havecharacterized the step-function dielectric lenses which are conventionalat the present time.

Still another object of the present invention resides in the manufactureof a novel dielectric lens which may be more readily fabricated, and atless cost, and which may be more readily tested and evaluated as a lensthan has been possible heretofore.

Still another object of the present invention resides in the provisionof a novel fabrication technique as well as a novel arrangement forfeeding dielectric materials, adapted to produce a continuously varyingdielectric constant (hence a continuously varying refractive index)across a body of dielectric material.

In achieving the various objects and advantages described above, thepresent invention contemplates the fabrication of a body of continuouslyvarying dielectric constant material formed from, for example, anartificial dielectric consisting of an array of randomly orientedmetallic particles supported by a low density dielectric material. Thesaid metallic particles may comprise insulated aluminum slivers,preferably of substantially needle shape having a length less thanone-eighth wavelength. The supporting matrix, in turn, may take the formof a low loss polystyrene foam similar to commercially availableArmalite, a trademark of the Armstrong Cork Company, Lancaster,Pennsylvania, fabricated from low density polystyrene beads orspheroids, also preferably less than one-eighth wavelength in size.Composite materials of this type simulate an actual dielectric whenimmersed in an electromagnetic field. In particular, in a dielectricmedium submicroscopic dipoles are set up by the impressed field andserve to alter the velocity of propagation of the wave; and in anartificial dielectric material of the type described, this principaleffect is achieved macroscopically by the conductive particles, i.e.,the randomly oriented metallic slivers of millimetric length act todelay waves of centimetric length (microwave situa tion).

In working with artificial dielectric materials of the type described, across feeding system or technique is preferably employed wherein a massof dielectric beads, interspersed with flakes or slivers of aluminum(whereby the composite mass exhibits a dielectric constant greater thanunity) is cross-fed with a lower index dielectric medium, comprising forexample plain polystyrene beads identical to those which serve as thevehicle for the metallic slivers. These two flowing streams ofdielectric material, respectively having dielectric constants greaterthan and substantially equal to unity, are fed into a charge box ofappropriate geometry (e.g., a substantially cylindrical charge box, inthe case of a cylindrical lens) through specially contoured gatesassociated respectively with the flowing streams; and the charge box isrotated as the crossfed material is fed therein. The gate contours,which will be described hereinafter, assure that the desiredcontinuously varying index, as well as a uniform depth of material iseffected in the rotating charge box. A similar cross-feeding techniquemay be employed to effect a charge of true dielectric material (ratherthan a sliver loaded artificial dielectric material) having the desiredcontinuously varying index. Such a true dielectric material maycomprise, for example, a mixture of polystyrene particles havingdifferent densities. Thus, again using a cross-feeding technique asdescribed, one of the two flowing streams may comprise foamedpolystyrene particles, and the other stream may comprise unfoamedpolystyrene particles; and these streams may, in the manner described,be fed to a substantially cylindrical charge box, e.g., via appropriatecontoured gates, to achieve the desired two-dimensional variation inrefractive index from the center of said charge box to its outer edge.In either case, i.e., using true or artificial dielectric materials, therefractive index variation is achieved by controlling and varying theloading concentration of the cross-fed materials.

The substantially smooth lay-up of dielectric material thus effected,having the desired continuous dielectric constant gradation therein, isthen fused into a unitary substantially cylindrical mass, e.g., by asteam molding process; and the unit thus produced may then be unmoldedand heat-treated for an appropriate extended period of time to effectthe removal of all moisture and also to insure dimensional stability inthe final device.

The resulting cylindrical unit has a continuously varying dielectricconstant whereby it may be used directly as a dielectric lens or, inconjunction with a conductive piece, as a microwave or radar reflector,e.g., in a buoy structure as a navigational aid. In the alternative,said unit can be associated with a dipole or other appropriate primaryfeed antenna positioned along the focal line of the lens as in theLuneberg embodiment, or at the focal point, as in the constant thicknessKelleher lens, to form a high gain antenna. Moreover, notwithstandingthe fact that the cylindrical unit produced by the technique of thepresent invention finds direct utility in a lens, antenna, or reflectorstructure, the unit may, if desired, be cut into subcomponents andreassembled in different configurations to provide more complex lensesnevertheless having desired substantially continuous dielectricgradations.

The foregoing objects, advantages, construction and operation of thepresent invention will become more readily apparent from the followingdescription and accompanying drawings, in which:

FIGURE 1 is an illustrative view of a substantially cylindricaltwo-dimensional dielectric lens fabricated in accordance with thepresent invention, depicting certain optical considerationscharacterizing one form of said lens;

FIGURES 2A, 2B and 2C illustrate an apparatus which may be employed infabricating the lens of the present invention, as well as successivesteps in the method of lens formation which characterizes a preferredembodiment of the present invention; and

FIGURE 3 is a top view of a portion of the system shown in FIGURE 2Aillustrating a preferred feeding arrangement employing contoured gatesin accordance with the present invention.

Referring initially to FIGURE 1, it will be seen that the lens L of thepresent invention may be substantially cylindrical in form having itsaxial center at O. The lens itself exhibits a substantially smooth andcontinuous variation in dielectric constant along the radii R of thelens between its center 0 and the outermost periphery of the lens. Thisvariation in dielectric constant may be accomplished, by the techniqueof the present invention, utilizing conventional dielectric materials;but in a preferred embodiment of the invention, the variation indielectric constant is achieved by use of an artificial dielectricmaterial comprising a matrix of near-unity dielectric constant materialsupporting a randomly oriented array of needle-like metallic particlestherein, with the concentration of said metallic particles in saidmatrix varying smoothly in substantially all directions from the centralaxis 0 of the lens to its outermost peripheral surface.

Moreover, in accordance with the present invention, the lens L is ofsubstantially constant density; and this must be distinguished fromvariable density materials and lens which have been suggestedheretofore, wherein attempted variations in dielectric constant areachieved by starting with a substantially constant density materialwhich is variably compressed to effect a dielectric gradation. Suchvarying density lenses, suggested heretofore in an effort to achieve adesired dielectric gradation, in addition to necessarily being shortcylinders due to nonlinearities inherent along the compression axis,have been found in practice to be anisotropic, i.e., the variation indielectric constant actually achieved has been found to be a function ofaspect, with a given incremental unit of the lens exhibiting differentdielectric constants in different directions. Such anisotropic variabledensity lenses cause rotation of the field vectors during thepropagation of energy through the lens medium, whereby the polarizationand velocity of a transmitted or received wave is altered in the lens;and this phenomenon has itself caused the resulting lens to depart fromthat contemplated in theory, since one theoretical advantage of, forexample, a Luneberg lens, is that the polarization of a propagated waveis not affected.

The lens L of the present invention, being of constant density, andachieving its dielectric gradation by a variation in loadingconcentration in a substantially constant density dielectric medium, isthus specifically different from variable density lenses suggestedheretofore, and obviates problems which have characterized such priorlenses.

The lens L of FIGURE 1 has been depicted as a Luneberg lens, and definesa line focus F at a surface of the lens. A dipole antenna A may bedisposed adjacent the surface of the lens along said line focus F forinjecting energy into the lens, or receiving signals therefrom; and inpractice said antenna A may comprise a wire or tube of appropriatecross-section arranged to be supported by the lens itself. In actualuse, the operating frequency may be such that the lens L is V2wavelength long in the direction indicated in FIGURE 1, in which casethe dipole antenna A could be employed as the primary (feed or pick-up)antenna; or the operating frequency could be such that the lens isseveral wavelengths long, in which case a pyramidal or sectoral hornantenna or the like could be employed. The natural directivity of thelens may, moreover, be improved in the former (or half wavelength) case,by adding a reflector element at a distance of approximately 0.2wavelength to the rear of the antenna A with said reflector element, ifemployed, being slightly greater than /2 wavelength long and beingphysically supported in place by means such as an appropriate insulatorstructure.

It will be appreciated, moreover, that the disposition of the antenna Aalong the focal line F has been shown at the external surface of thelens on the premise that the lens L is of the Luneberg type; and thisparticular type of lens will in fact be discussed hereinafter. Thevarious techniques to be described, however, can be employed infabricating lenses of the type shown at L in FIGURE 1 wherein, byappropriate alteration of the loading concentration of the artificialdielectric material employed, the optics of the lens vary in some mannerother than that suggested by Luneberg, and in accordance with thesuggestions of other workers in the field. By appropriate variation ofthe dielectric gradation, the focus F may actually occur for examplealong a line F internal of the lens, in which event the antenna A may bephysically embedded in the lens L, along the line F. Similarly, by othersuitable modifications, the location of the focus may be caused to occuralong a line external of the outer lens surface, in which event theantenna A may be physically supported along this alternative line focusin proper spaced relation to the exterior lens surface, e.g., byappropriate insulator structures. In still other embodiments, theconstant thickness Kelleher lens for example, the focus exists on a linepassing through the geometric axis of the cylinder, and an appropriatefeed antenna placed at the focal point would, in such a case, provideplane wave propagation (or reception) in a direction normal to the planesurfaces of the lens. The present invention, being concerned with thelens itself, may therefore be used ultimately in any of these variousmanners, and with any of the various feed structures and dispositionswhich one skilled in the art may wish to select.

Considering now the actual lens L shown in FIGURE 1, and assuming thatsaid lens L is, for purposes of the instant description, of the Lunebergtype, the refractive index (n) of the lens should, as mentionedpreviously, vary as a function of the lens radial coordinates (r) inaccordance with Equation 1, supra. If this relationship is achieved, anyrays entering the lens along its focal line P will be focussed by thelens L into parallel rays so as to emerge from the lens as a plane wavefront. In particular, as illustrated in FIGURE 1, any single ray leavingthe source at focus F at an angle 0 will be radiated from the lens L ata point P so positioned that the radius OP of the lens also forms anangle 0. Similarly, since reciprocity applies, any electromagneticenergy in the form of a plane wave impinging on the lens L will berefracted and concentrated at the line focus F. These relationshipscontemplated by theory can be achieved, however, only if the refractiveindex varies in accordance with Equation 1, supra; and saidrelationships have thus far been only approximated by the use ofstepped-index lenses, or by variable density lenses, with thedisadvantages of each having already been discussed.

In accordance with the present invention, a highly improved lens,characterized by a smoothly and continuously varying dielectric constantin a substantially constant density medium, is fabricated by a novelmethod thereby to obviate the various problems and disadvantagesdescribed above. The two-dimensional continuously graded material whichcharacterizes lens L can be effected by various techniques operative toachieve a smooth variation in loading concentration in radial directionsof the lens; but a highly preferred such technique is that illustratedin FIGURES 2A through 2C and 3, wherein a blend feeder employing adilution technique is used in the lens fabrication. To this effect, apair of hoppers 10 and 11, associated with a pair of aligned conveyors12 and 13 and with a pair of appropriately contoured gates 14 and 15,effect a substantially constant flow of varyingly loaded dielectricmaterial to a central discharge point or line 16. Hopper 10 contains apre-mixed blend 17 of polystyrene beads and aluminum slivers, having adielectric constant greater than 1; and in particular having adielectric constant of e the maximum dielectric constant required by thefinal lens. In a typical case, this high index blend 17 may have adielectric constant of 1.92. The hopper 11 in turn contains a diluent17a having a low index dielectric material therein comprising, forexample, plain polystyrene particles identical to those which serve asthe vehicle for the metalIic slivers in blend 17; and in a typical case,the dielectric constant e of the plain polystyrene beads in hopper 11may be 1.03.

While it has been indicated that the mixed blend 17 is contained in ahopper 10 as a pre-mixed batch of material, even more accuracy in thefinal product can be achieved by replacing hopper 10 with a preliminarypair of conveyors and hoppers adapted, by a dilution technique similarto that shown in FIGURE 2A, to effect a highly accurate blend having thedesired dielectric constant, e.g., 1.92. To this effect, the hopper 10may be replaced by a further pair of auxiliary conveyors associated inturn with a further pair of hoppers. One of these further hoppers maycontain a batch of blended polystyrene particles and aluminum slivershaving a dielectric constant higher than that desired of the material onconveyor 12; and the second of these hoppers may contain plainpolystyrene beads. The material in these two hoppers may be fed alongsaid two auxiliary conveyors through automatically controlled gates, thevertical positions of which may be variably changed with changes in theactual dielectric constant of the material passing along at least one ofsaid conveyors. The gate control can be achieved by an appropriatesensing circuit, all as shown, for example, in my prior copendingapplication Serial No. 52,932 filed August 30, 1960 for Admittance Meterand Dielectric Control System.

With this further refinement the initially mixed blend would bedischarged from the aforementioned auxiliary conveyors onto conveyor 12at a position equivalent to the discharge end of hopper 10; and by thearrangement described, an extremely accurate control of the dielectricconstant of the mixed blend passing along conveyor 12 would then beachieved. This, however, represents a refinement which is not essentialto the present invention; and the actual arrangement shown in FIGURE 2A,utilizing a pre-mixed blend in hopper 10, gives entirely adequateresults.

The material in the hoppers 10 and 11 passes, as described previously,through contoured gates 14 and 15 to discharge point 16 whereupon theresulting mixed blend of relatively high index and relatively low (ornearunity) index dielectric material is dumped into a charge box 18 (ormold) having a substantially cylindrical recess 19. The width of each ofconveyors 12 and 13, and the length of contoured gates 14 and 15, ischosen to be equal to either the radius or the diameter of the finalplanned lens; and is similarly chosen to equal a radius or diameter ofthe recess 19 in charge box 18. Radial length gates and conveyors havebeen shown in the drawings; but each radial length gate may be expandedto diameter length by adding, to each such gate, a further gate sectioncontoured as the mirror image of the gate actually shown and to bedescribed.

In the case of the radial width conveyors and gates, and as best shownin FIGURE 3, the aligned conveyors 12 and 13 are so positioned withrespect to charge box 18 that their respective edges lie between thecenter and outer periphery of recess 19. The blend of materialdischarged at 16 into recess 19 is therefore laid up in said recess 19along a radius of the recess. During this lay up, charge box 18 isrotated as at 20 to distribute the material evenly and with circularsymmetry along the complete circular cross section of recess 19, withthe rate of rotation merely being sufficiently fast to assure a smoothand symmetrical lay up of the dielectric material in charge box 18.

The desired variation in dielectric constant across the radii of thegranular substantially cylindrical mass deposited in recess 19 iseffected by reason of the aforementioned rotation of charge box 18,cooperating with the contoured gates 14 and 15. The actual contour ofthese gates is selected in accordance with the particular type of lenswhich it is desired to finally produce; and in the case of a Luneberglens, the contours of said gates 14 and 15 may be similar to those shownin FIGURE 3. In such a Luneberg lens, the refractive index (n) shouldvary in accordance with Equation 1 given previously; and this may beexpressed also as a variation in dielectric constant (c) by theequation:

R=the lens radius (or the conveyor belt width in the arrangement ofFIGURES 2A and 3);

r=the radial variable in planes parallel to the bottom of recess 19 (seealso, FIGURE 1); and

c=th relative dielectric constant of the material corresponding to anyparticular point r.

where,

For such a relationship, the contour of gate 14, associated with therelatively high index blend 17 in hopper 10 can be expressed by theequation:

where,

R=the radius of the lens; x=the distance variable (corresponding to theradial 8 variable) in directions across conveyor belt 12 (see FIGURE 3)from the center of recess 19; K=a feeder constant, equal to where H isthe maximum gate opening achievable; and h =the variable height of theaperture in gate 14.

In addition, the contour gate 15, associated with the hopper 11containing near-unity dielectric constant plain polystyrene beads, canbe expressed by the equation:

where,

h is the variable height of the aperture in gate 15.

Each of the other variables in Equation 4 have been discussedpreviously.

The two gates 14 and 15 are maintained in fixed position relative toconveyors 12 and 13, and provide a substantially constant (with time)flow of material at discharge point 16. In addition, the contours of thetwo gates are so selected as to achieve the desired uniform gradation indielectric constant across the radius (or diameter) of recess 19 as thecharge box 18 is rotated. In effect, gates 14 and 15 achieve thisdesired gradation in dielectric constant by effecting an appropriatevariation in the loading of the blend across the radius R of recess 19,at position 16. The said gates 14 and 15 moreover cooperate with oneanother to achieve a combined flow having a smoothly varying rate atdifferent points along the radius of recess 19; and the actualdeposition of material follows the substantially triangularconfiguration shown at 21 in FIGURE 3, comprising substantially zeroflow at the center of the recess 19 and maximum flow at thecircumference of said recess 19. This triangular dumping or depositionof the granular dielectric material assures that a substantially smoothlay-up of said material is achieved in cylindrical recess 19 as chargebox 18 is rotated.

It will be appreciated, of course, that arrangements alternative tothose shown in FIGURES 2A and 3 are available to achieve substantiallysimilar final results. By way of example, the conveyor belts 12 and 13,rather than having a width substantially equal to the radius of recess19, and rather than being associated with contoured gates such as 14 and15, can be replaced by small capacity feeders having a width much lessthan the radius of the charge box. With this alternative arrangement,the actual dielectric constant of the material flowing along the smallcapacity feeders can be appropriately programmed as required for a givenlens configuration, e.g., in accordanoe with Equations 3 and 4 for aLuneberg lens; and the charge box can also be position-programmed, i.e.,rotated and translated, with corresponding changes of the dielectricconstant of the material flowing toward the charge box, all to achievethe necessary smooth lay-up and substantially continuous dielectricvariation which is desired.

After the charge box 18, and particularly the recess 19, has been filledwith material in accordance with the technique described (and it will beappreciated, of course, that charge box 18 may itself comprise a mold ifpracticable) the lay-up may then be fused into a complete andhomogeneous cylindrical unit, e.g., by a steam molding process. Anapparatus such as that shown in FIGURE 28 may be employed to thiseffect, whereby the charge 22 in the final lay-up may be subjected tosteam flow through pipe 23, the opposite side of the apparatus beingcoupled to a vacuum exhaust 24. In such a steam molding step, thearrangement shown in FIGURE 28 is particularly desirable since itachieves steam flow in directions normal to the lens surface; and suchflow is highly preferred in order that any density shifts which mightoccur during fusion may be accommodated from a dielectric standpoint inthe final lens.

After completion of the fusion process, the fused lens 25 may beunmolded as shown in FIGURE 2C; and said lens 25 may then beheat-treated for an extended period of time to eifect removal of allmoisture therefrom, as well as to insure dimensional stability. In atypical case (e.g., using a polystyrene matrix), moisture removal andstress relief can be effected in a stabilization room wherein fused lens25 is subjected to a constant temperature of approximately 170 F. for aperiod of three to seven days.

The resulting mass 25 is, it will be appreciated, of cylindricalconfiguration and defines a smoothly varying dielectric constantgradation along its radii. The outermost surface of cylindrical mass 25is, as a result of the contours of gates 14 and 15, substantiallycomprised of plain polystyrene beads only whereby this outer surface hasa dielectric constant which closely approximates that of surroundingair. In the final lens, dielectric discontinuities at the outer surfaceof the lens are thus substantially eliminated, thereby minimizing lossesas energy passes into or out of the lens. It will be further appreciatedthat the graded cylinder 25 is formed readily and relativelyinexpensively by a unique and reproducible process. Accordingly, oncethe initial fabrication techniques shown in FIGURES 2A through 2C, and 3has been finalized, highly uniform lenses can be made in massproduction.

It should further be noted that, once the cylindrical lens 25 has beencompleted, it is immediately possible and indeed desirable to test thecylinder at the ultimate frequency of operation. By such a testingtechnique, the lens quality and focal point can be readily establishedwithout need of the costly and time-consuming assembly steps which havecharacterized lens fabrication techniques suggested heretofore.Moreover, if the lens characteristics are found to depart from thosedesired, the artificial dielectric media, and/or the loadingconcentration therein, can be appropriately changed before continuingwith the fabrication of further lens units. This, in itself, representsa significant additional saving in money and labor over techniquessuggested heretofore, since it assures proper and consistent performanceof mass produced lenses. By such a testing technique, the actualdielectric gradation across the lens can be determined; and if it isfound that this gradation departs from that actually desired, simpleadjustments of the contours of gates 14 and 15 can be effected to takecare of such deviations at the particular point of lay-up where thediscrepancy has occurred. With such adjustment of the gate contourand/or dielectric media, the accuracy of subsequent lenses can thus beimmediately assured; and this accuracy will persist as multiple suchlenses are fabricated, a result impossible heretofore.

The two-dimensionally graded cylinder 25, produced by the techniquedescribed above, can itself be used directly as a lens element, such asthat indicated at L in FIG- URE 1, and comprises in this respect anoperable two-dimensional Luneberg lens differing from prior suchtwo-dimensional lenses suggested heretofore in the fact that it isinherently circularly symmetric, exhibits a substantially smoothdielectric gradient in a substantially constant density media, and hasno interior interfaces or dielectric discontinuities. The cylindricallens of the present invention, moreover, differs from previousdielectric lenses of cylindrical configuration, of both stepped-indexform and otherwise, in that such prior lenses have ordinarily taken theform of extremely short cylinders having a height much less than theirdiameter, whereby a severe limitation has been imposed on the type offeed antenna which could be employed. This difficulty is avoided by thepresent invention, since the cylindrical mass 25 may readily have aheight-diameter ratio which is considerably greater than that which hasbeen possible heretofore; and

in one practical lens embodiment, fabricated by the described technique,the cylindrical mass 25 was approximately eighteen inches in height andapproximately three feet in diameter. The technique described may,moreover, be utilized to form lenses of different sizes, both larger andsmaller than that mentioned; and the largest lens which can befabricated is limited only by such physical limitations as the size ofthe molds 18 which are available to receive the initial charge. Indeed,the substantially circular cross-section mass could be fabricated andmolded as a continuum (rather than as units) in which case cylinders ofappropriate height can be produced simply by cutting at appropriatepoints along the length of the fused mass. The present invention isparticularly useful in the construction of relatively small diameterlenses (e.g., less than ten feet in diameter); but there is notheoretical restriction on the lens size or electrical or dimensionalconfiguration which may be produced.

The cylindrical two-dimensionally graded mass 25 may moreover beutilized as a starting material in the fabrication of more complex lensforms, e.g., one or more such masses 25 can be severed into variouslyshaped subcomponents which may thereafter be reassembled in differentconfigurations when more complex lens formations are desired or requiredby a particular installation. The lens or mass 25 may, in addition, beprotected, subsequent to its final fabrication, by an appropriate outershell such as a thin glass-reinforced polyester shell, so as to reducepossible deterioration or splintering of the lens and to also render thelens substantially impervious to sun, water, and marine parasites (inthe case of marine use, e.g., as a navigational aid or buoy).

Still other variations and modifications will be suggested to thoseskilled in the art. It must, therefore, be understood that while I havethus described a preferred technique and embodiment of the presentinvention, all such variations and modifications as are in accord withthe principles of the present invention are meant to fall within thescope of the appended claims.

Having thus described my invention, I claim:

1. The method of fabricating a mass of dielectric material having asubstantially continuous variation in dielectric constant whichcomprises the steps of cross-feedin g a granular dielectric material ofnear-unity dielectric constant with a granular dielectric material ofhigher dielectric constant, said cross-feeding being effected into andalong a radius of a substantially cylindrical charge box with varyingamounts of said materials being mixed with one another at differentpoints along said radius, rotating said charge box during saidcross-feeding to build up a circularly symmetrical mass of saidcross-fed granular material, and fusing the granular material in saidcharge box into a homogeneous substantially cylindrical mass oftwo-dimensionally graded dielectric material.

2. The method of claim 1 wherein said fusing step comprises subjectingthe cross-fed material in said charge box to steam directed normally tothe outermost faces of said circularly symmetrical mass.

3. The method of claim 1 wherein said higher dielectric constantmaterial comprises a conductive sliver loaded artificial dielectricmaterial, said cross feeding step including the step of feeding saidmaterials through differently contoured gates to vary the amounts ofsaid two dielectric materials which are mixed with one another along theradius of said charge box thereby to vary the loading concentration ofsaid cross-fed material along said radius.

4. The method of claim 3 wherein said cross feeding step comprisesfeeding said higher dielectric constant material through a contouredgate having a height, h,, substantially defined by the equation:

K 2 e is) and feeding said near-unity dielectric material through adifferently contoured gate having a height, h substantially defined bythe equation:

where c is the index of said higher dielectric constant material, R isthe radius of said charge box, x is the di' mension of the feed pointalong said radius, and K is a constant.

5. The method of fabricating a mass of dielectric material whichcomprises feeding a first dielectric material of relatively highdielectric constant toward a discharge line via a first contoured gate,feeding a second dielectric material of relatively low dielectricconstant toward said discharge line via a second differently contouredgate, mixing said first and second dielectric materials at saiddischarge line thereby to produce a mass of varying dielectric constantmaterial having a variation in dielectric constant along said linedetermined by the relative dielectric constants of said first and secondmaterials and by the differences in contour of said gates, collectingsaid mixed varying constant dielectric material in a collectionreceptacle while effecting relative motion between said receptacle andsaid discharge line, and thereafter fusing the collected material.

6. The method of claim 5 wherein said step of effecting relative motioncomprises rotating said receptacle during said collection to build up acircularly symmetrical mass of said varying constant dielectricmaterial.

7. The method of claim 6 wherein said receptacle is substantiallycylindrical in configuration, said mixing and collection steps beingeffected along a radius of said cylindrical receptacle.

8. The method of claim 5 wherein said first dielectric materialcomprises a mass of polystyrene beads having conductive metallicparticles mixed therewith, said second dielectric material comprisingplain polystyrene beads of the same type as comprises the vehicle forsaid metallic particles.

9. The method of claim 5 wherein said fusing step comprises steammolding the material collected in said receptacle into a homogeneousmass, and thereafter subjecting said fused homogeneous mass to heat foran extended period of time to stablize the dimensions of said mass.

10. The method of fabricating a mass of varying index dielectricmaterial which comprises feeding a first rela' tively high indexdielectric material toward a predeter- 12 mined discharge line having alength R, the amount I], of said first material being varied along saidline R substantially in accordance with the equation:

where x is the dimension along said line R from a predetermined endthereof and K is a constant, feeding a second lower index dielectricmaterial toward said discharge line, the amount I1 of said secondmaterial being varied along the length R of said line substantially inaccordance with the equation:

where e is the dielectric constant of said first material, mixing saidfirst and second variably fed materials with one another along thelength R of said discharge line, collecting said mixed materials in acollection receptacle while effecting relative motion between saidreceptacle and said discharge line, and fusing the collected materialinto a homogeneous mass.

11. The method of fabricating a mass of varying index dielectricmaterial which comprises feeding a first relatively high indexdielectric material toward a discharge line at a first varying ratealong said line, feeding a second lower index dielectric material towardsaid discharge line at a second varying rate, different from said firstvarying rate, along said line, mixing said first and second variably fedmaterials with one another along said line, collecting said mixedvariably fed materials in a receptacle while effecting relative motionbetween said receptacle and said line thereby to achieve a mass ofmaterial having a varying loading concentration which concentration isthe joint function of both said first and second varying feed rates, andfusing the collected material into a solid mass.

References Cited by the Examiner UNITED STATES PATENTS ROBERT F. WHITE,

HERMAN K. SAALBACH, Examiner.

W. K. TAYLOR, M. R. DOWLING, Assistant Examiners.

Primary Examiner.

1. THE METHOD OF FABRICATING A MASS OF DIELECTRIC MATERIAL HAVING ASUBSTANTIALLY CONTINUOUS VARIATION IN DIELECTRIC CONSTANT WHICHCOMPRISES THE STEPS OF CROSS-FEEDING A GRANULAR DIELECTRIC MATERIAL OFNEAR-UNITY DIELECTRIC CONSTANT WITH A GRANULAR DIELECTRIC MATERIAL OFHIGHER DIELECTRIC CONSTANT, SAID CROSS-FEEDING BEING EFFECTED INTO ANDALONG A RADIUS OF A SUBSTANTIALLY CYLINDRICAL CHARGE BOX WITH VARYINGAMOUNTS OF SAID MATERIALS BEING MIXED WITH ONE ANOTHER AT DIFFERENTPOINTS ALONG SAID RADIUS, ROTATING SAID CHARGE BOX DURING SAIDCROSS-FEEDING TO BUILD UP A CIRCULARLY SYMMETRICAL MASS OF SAIDCROSS-FED GRANULAR MATERIAL, AND FUSING THE GRANULAR MATERIAL IN SAIDCHARGE BOX INTO A HOMOGENEOUS SUBSTANTIALLY CYLINDRICAL MASS OFTWO-DIMENSIONALLY GRADED DIELECTRIC MATERIAL.